Article
MSC:
37J15,
37J99,
58F05,
70H03,
70H35,
70S05,
70S10 | MR 1618723 | Zbl 0901.58016 | DOI: 10.21136/MB.1998.126290
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Keywords:
Lagrangian formalism; classical field theory; Noetherian symmetries
Lagrangian formalism; classical field theory; Noetherian symmetries
Summary:
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to have a geometric point of view of the usual Noetherian symmetries for classical field theories and strongly supports the usefulness of the above mentioned differential form.
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